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Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2011 (English)In: Moscow Mathematical Journal, ISSN 1609-3321, Vol. 11, no 3, 547-560 p.Article in journal (Refereed) Published
Abstract [en]

In their classic 1914 paper, Polya and Schur introduced and characterized two types of linear operators acting diagonally on the monomial basis of R[x], sending real-rooted polynomials (resp. polynomials with all nonzero roots of the same sign) to real-rooted polynomials. Motivated by fundamental properties of amoebae and discriminants discovered by Gelfand, Kapranov, and Zelevinsky, we introduce two new natural classes of polynomials and describe diagonal operators preserving these new classes. A pleasant circumstance in our description is that these classes have a simple explicit description, one of them coinciding with the class of log-concave sequences.

Place, publisher, year, edition, pages
2011. Vol. 11, no 3, 547-560 p.
Keyword [en]
Multiplier sequence, discriminant, amoeba, chamber
National Category
URN: urn:nbn:se:su:diva-49778ISI: 000300365900008OAI: diva2:379431
Available from: 2010-12-31 Created: 2010-12-17 Last updated: 2012-04-16Bibliographically approved

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